The filing submitted by the multi-billionaire’s lawyers asked for the months-old case to be dropped without offering any reason for the move.
It came just a day before the court was expected to hear the ChatGPT-developer’s bid to have the case dismissed.
BBC News has contacted Mr Musk’s lawyer and OpenAI for comment.
The latest filing asked for the case’s dismissal “without prejudice”, meaning Mr Musk could still reactivate it at a later stage.
The Tesla boss filed the lawsuit against OpenAI at the end of February this year, arguing the company he had helped found in 2015 had deviated from its altruistic goals to focus on making money.
OpenAI countered that Mr Musk had previously backed the idea of a for-profit structure and even suggested a merger with his electric car firm Tesla.
The feud intensified earlier this week after Apple unveiled a partnership with OpenAI to boost its Siri voice assistant and operating systems with OpenAI’s ChatGPT chatbot.
After the announcement, Mr Musk posted several messages on his social media platform X, formerly known as Twitter, criticising the tie-up.
One of the posts ended with the words: “Apple has no clue what’s actually going on once they hand your data over to OpenAI. They’re selling you down the river.”
However, investors seemed to welcome the news, as Apple’s stock market value rose to a record high above $3tn.
Mr Musk started his own AI company, called xAI, in July 2023, which he said would aim to “understand reality”.
In November that year, xAI launched Grok, a chatbot with “a little humour”, in a bid to rival the likes of ChatGPT.
